Copying mask key frames but different shape
In the movie clip editor.

Select the vertices of the mask you want to move, then shift-select one of the control points of the other mask and press Ctrl+P to parent. 

For example: this mask is parented to a tracking point.



If I create a second mask, and parent it to one of the points of the first mask, then they both move together.



If you don't want to create a new mask but duplicate an existing one. Just select the mask, and hit shift+D to duplicate it and move it where you want, all of the atributes and keyframes of the original mask will be duplicated.